Method for processing data to find intersection between rational parametric surfaces, device, and medium

Abstract

The present disclosure provides a method for processing data to find an intersection between rational parametric surfaces, a device, and a medium. The method for processing data to find the intersection between rational parametric surfaces includes: determining four-dimensional parametric curve data; decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data; decomposing each of the plurality of first strongly monotonic curve segment data into at least one second strongly monotonic curve segment data; and determining a point distance between two adjacent points of each of the at least one second strongly monotonic curve segment data in a corresponding three-dimensional model space, so as to find the intersection between rational parametric surfaces.

What is claimed is: 
     
         1 . A method for processing data to find an intersection between rational parametric surfaces, comprising:
 determining four-dimensional parametric curve data;   decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data;   decomposing each of the plurality of first strongly monotonic curve segment data into at least one second strongly monotonic curve segment data; and   determining a point distance between two adjacent points of each of the at least one second strongly monotonic curve segment data in a corresponding three-dimensional model space, so as to find the intersection between rational parametric surfaces.   
     
     
         2 . The method of  claim 1 , wherein the determining four-dimensional parametric curve data comprises:
 determining the four-dimensional parametric curve data based on received first rational parametric surface data and second rational parametric surface data.   
     
     
         3 . The method of  claim 1 , further comprising: before decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data,
 determining four-dimensional tangent vector data and three-dimensional tangent vector data, wherein the four-dimensional tangent vector data corresponds to the four-dimensional parametric curve data, and the three-dimensional tangent vector data corresponds to three-dimensional parametric curve data formed by mapping the four-dimensional parametric curve data into the three-dimensional model space.   
     
     
         4 . The method of  claim 1 , wherein the decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data comprises:
 tracing the four-dimensional parametric curve data from a predetermined starting point corresponding to the four-dimensional parametric curve data, and in response to a decomposed curve segment meeting a predetermined first lemma condition, determining the decomposed curve segment as one of the plurality of first strongly monotonic curve segment data, wherein the decomposed curve segment corresponds to an ending point meeting a first predetermined step length with the predetermined starting point.   
     
     
         5 . The method of  claim 4 , wherein the decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data further comprises:
 tracing the four-dimensional parametric curve data from a predetermined starting point corresponding to the four-dimensional parametric curve data, and in response to a decomposed curve segment meeting a first predetermined cycle condition, determining a critical point of the decomposed curve segment, wherein the decomposed curve segment corresponds to an ending point meeting the first predetermined step length with the predetermined starting point; and   determining, in response to a first decomposed curve segment and a second decomposed curve segment meeting a second lemma condition, the first decomposed curve segment and the second decomposed curve segment as two of the plurality of first strongly monotonic curve segment data, and continuing to trace the four-dimensional parametric curve data by using the ending point of the decomposed curve segment as a starting point, wherein the first decomposed curve segment corresponds to the predetermined starting point of the decomposed curve segment and the critical point, and the second decomposed curve segment corresponds to the critical point and the ending point of the decomposed curve segment,   wherein the first lemma condition and the second lemma condition are related to four-dimensional tangent vector data corresponding to the four-dimensional parametric curve.   
     
     
         6 . The method of  claim 5 , wherein the decomposing the four-dimensional parametric curve data into a plurality of first strongly monotonic curve segment data further comprises:
 re-tracing the four-dimensional parametric curve data with a second predetermined step length from the predetermined starting point, in response to the first decomposed curve segment and the second decomposed curve segment not meeting the second lemma condition or in response to failing to determine the critical point,   wherein the second predetermined step length is half of the first predetermined step length.   
     
     
         7 . The method of  claim 1 , wherein the decomposing each of the plurality of first strongly monotonic curve segment data into at least one second strongly monotonic curve segment data comprises:
 decomposing, according to a third lemma condition, each of the plurality of first strongly monotonic curve segment data into at least one second strongly monotonic curve segment data in a corresponding three-dimensional model space,   wherein the third lemma condition is related to three-dimensional tangent vector data corresponding to three-dimensional parametric curve data in a three-dimensional model space corresponding to the four-dimensional parametric curve.   
     
     
         8 . An electronic device, comprising:
 one or more processors; and   a memory for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, are configured to cause the one or more processors to implement the method of  claim 1 .   
     
     
         9 . A computer-readable storage medium having computer-executable instructions, wherein the instructions when executed are configured to implement the method of  claim 1 .